Small-$x$ resummation in coefficient function for differential heavy-quarks production

High-energy logarithmic correction are enhanced when the ratio, $x=\frac{Q^2}{s}$ between the typical energy scale of a scattering process $Q$ and the total centre of mass energy available $s$ is small. We discuss recent developments on their resummation in differential cross sections in rapidity, transverse momentum and invariant mass and their application to heavy flavour production at the LHC.